Dynamic Modeling of Automatic Machines for Design and Control

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction

   Juan Carlos Jauregui-Correa

   Abstract

   This chapter introduces the concepts that will be developed throughout the book. Describes general aspects of an automatic machine, the purpose of modeling and analyzing dynamic systems, and some of the fundamental concepts of simulation. The simulation of automatic machines starts from the physical description of their main elements. This mathematical model describes the dynamic response of each component, the integration of the individual contributions to the dynamic of the entire system, and the implications of the dynamic response for controlling or designing a machine. This chapter also gives an overview of the elements that compose an automatic machine and describes the content of every chapter.

3. Chapter 2. Multibody Dynamics

   Juan Carlos Jauregui-Correa

   Abstract

   This chapter presents an overview of the basis for multibody dynamics. The best representation of an automated machine is analyzing it as a multibody system composed of rigid masses interacting through elastic elements and receiving external forces from different actuators. The first step in determining the dynamic equations is the definition of the kinematic equations. The basic concepts for defining the kinematic equations are position, velocity, and acceleration, and these terms are found using the concept of the generalized coordinate. The first part of this chapter defines the generalized coordinates, the definition of motion constraints, and the generalized velocities and accelerations. The chapter continues with the derivation of kinetic and potential energy and concludes with the Lagrange equation.

4. Chapter 3. Actuators

   Juan Carlos Jauregui-Correa

   Abstract

   This chapter presents the dynamic models of automatic machines’ most commonly used actuators. The models are developed based on their physics and treated as lumped mass systems or discrete systems. Only DC electric motors are presented; they represent the majority of electric motors used in automatic machines, and their dynamic behavior is the basis for analyzing servo motors. The dynamic response of DC motors begins with the electro-mechanical interaction and the derivation of the electric and mechanical differential equations. Pneumatic systems are analyzed from the thermodynamics of the working fluid and its energy interaction with the moving parts, plus the electromagnetic performance of the actuating valves; while hydraulic systems are a particular case considering that the fluid is incompressible. These models result in a set of differential equations that describe the actuators’ dynamic behavior.

5. Chapter 4. Sensors

   Juan Carlos Jauregui-Correa

   Abstract

   This chapter describes the sensor’s time response and its effect on the machine’s dynamic. It also describes the dynamic response of the most common sensors utilized in automatic machines and specifies accuracy and time response values. The sensors in this chapter are related to the position and speed measurement and control, identifying other characteristics such as vibration, process sensors, and the application of vision systems in automatic machines. The main contribution of this chapter is the definition of the time response and accuracy and its effect on the overall dynamic responses since these parameters are critical in the sequence response of the entire machine.

6. Chapter 5. Dynamic Models of Machine Elements

   Juan Carlos Jauregui-Correa

   Abstract

   This chapter includes the dynamic models of the machine elements that connect the actuators with the end effects. Chapter 2 described the basic dynamic modeling of automated machines. The modeling was developed using the fundamental concepts of multibody dynamics. In most applications, the elements that connect different components of the automated machines are represented as elastic joints o connections. This chapter describes the dynamic parameters of those elements representing them as an elastic connection producing a simplified description of the reacting forces as linear or nonlinear elastic functions. This simplification reduces the complexity of the dynamic analysis of complex automated machines without losing accuracy. The elements described are gears, rolling components (ball bearings, roller screws, slide bearings), belts and conveyors.

7. Chapter 6. Dynamic Response of Mix Systems

   Juan Carlos Jauregui-Correa

   Abstract

   The dynamic models are complex and highly nonlinear; thus, finding an automatic machine's time response requires numerical solutions. There are several forms of finding the time response of complex systems, in particular when combining different components. This chapter presents the dynamic response of automatic machines widely used in industrial applications. The dynamic equations were derived in previous chapters, and the solution is found using Simulink™. Examples include power supply mechanisms by electric motors, gear transmissions, belt transmissions, ball screw systems, and pneumatic applications. It also includes special codes for simulating the nonlinear terms of the gear mesh stiffness, ball bearing stiffness, and the bearing.

8. Chapter 7. Transfer Function

   Juan Carlos Jauregui-Correa

   Abstract

   Analyzing the simulation results is a crucial factor for determining an automatic machine's stability, accuracy, and repetitiveness. The operating conditions depend on many uncontrolled factors, such as ambient temperature, noise, surrounding vibration, and electric power fluctuations. The effect of these factors can be diminished if the time response of every component is known since the command sequence can be adjusted to avoid overlapping the transient responses with steady-state conditions. For linear systems, the time response can be determined from the transfer function, but for nonlinear systems, the transient response must be determined from simulation results. This chapter presents the application of the transfer function to simple cases and other techniques for the analysis of complex nonlinear systems. This chapter also includes the relationship between the dynamic simulation and the controller and recommendations for reviewing the definition of command sequence for better controlling and automatic machine.

9. Chapter 8. Simulation

   Juan Carlos Jauregui-Correa

   Abstract

   The importance of solving dynamic models with simulation tools has been discussed. This chapter presents different numerical integration techniques widely used for simulating dynamic equations. It also presents the advantages and disadvantages of the numerical methods and describes the mathematical background and the algorithm procedures. The second part of this chapter presents the most commonly used signal analysis techniques for understanding the dynamic behavior of automatic machines. It includes the traditional Fast Fourier Transform and the methods for constructing time–frequency maps, namely spectrograms, such as the Short Time Fourier Transform, the Continuous Wavelet Transform, and the Discrete Wavelet Transform.